# what subset $y$ of the set $N_0$ define the relations $\{ 3,5 \} \subseteq y \subseteq \{1,3,5,7 \}$?

what subsets $y$ of the set $N_0$ define the relations $\{ 3,5 \} \subseteq y \subseteq \{1,3,5,7 \}$?

what sets $y$ define the relation $y \subseteq \{a \}$ where $\{a \}$ is a given single set?

Could anyone give some hints and ideas for finding this subsets?

## 1 Answer

Hint: review the definition. Subset or equal $(\subseteq)$ means that all the elements of the set on the left are also elements of the set on the right. The set on the right may have additional elements as well. You have two numbers that must be in $y$ and some others that are optional. Can you identify those?

• its the $N without 1,3,5,7$? – Legolas Nov 19 '15 at 16:28
• No. If $8$ is an element of $y$, you will not have the right subseteq relation holding. – Ross Millikan Nov 19 '15 at 16:35
• 1,3,5,7 and 3,5 then? – Legolas Nov 19 '15 at 16:44
• That is correct – Ross Millikan Nov 19 '15 at 17:25
• Then the only subsets are the empty set and $\{a\}$. The usual term is a "singleton" set. – Ross Millikan Nov 19 '15 at 18:30